Let's break down the expression step by step.
The original expression is:
\[ 55 \times 13 \div 7 \div 11 \times 6 \div 13 \times 15 \div 5 \times 21 \div 3 \div 9 \div 5 \]
Following the order of operations, we will perform the calculations step by step:
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Calculate \( 55 \times 13 \): \[ 55 \times 13 = 715 \]
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Divide \( 715 \) by \( 7 \): \[ 715 \div 7 = 102.142857 \text{ (approximately 102.14)} \]
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Divide the result by \( 11 \): \[ 102.142857 \div 11 = 9.25 \]
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Multiply by \( 6 \): \[ 9.25 \times 6 = 55.5 \]
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Divide by \( 13 \): \[ 55.5 \div 13 = 4.285714 \text{ (approximately 4.29)} \]
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Multiply by \( 15 \): \[ 4.285714 \times 15 = 64.28571 \text{ (approximately 64.29)} \]
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Divide by \( 5 \): \[ 64.285714 \div 5 = 12.8571428 \text{ (approximately 12.86)} \]
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Multiply by \( 21 \): \[ 12.8571428 \times 21 = 270 \]
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Divide by \( 3 \): \[ 270 \div 3 = 90 \]
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Divide by \( 9 \): \[ 90 \div 9 = 10 \]
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Finally, divide by \( 5 \): \[ 10 \div 5 = 2 \]
The final result of the expression is:
\[ \boxed{2} \]